The ﬂow of viscous ﬂuid from a line source on an inclined plane containing a topographic depression is studied using a lubrication model. The steady ﬂow is perturbed by the depression. We focus on the regime in which the ﬂow thickness is small relative to the length scale of the depression. For shallow depressions, the ﬂow is only slightly perturbed. However, for deeper depressions a large pond of ﬂuid with a horizontal free-surface is observed. This ponding of ﬂuid is associated with the topography having uphill regions, which in the absence of inertia can only be surmounted by developing a deep ﬂuid layer. The accumulation of ﬂuid in the depression leads to a focusing of the ﬂow, which is observed even far downstream of the depression.
|Number of pages||4|
|Publication status||Submitted - 20 Jul 2020|
|Event||Australasian Fluid Mechanics Conference - Brisbane, Australia|
Duration: 6 Dec 2020 → 10 Dec 2020
Conference number: 22
|Conference||Australasian Fluid Mechanics Conference|
|Period||6/12/20 → 10/12/20|